But I don't understand parts C, D, and E. What does p=2p(1,1) mean in relation to C, D, and E?

If I ignore the part about p=2p(1,1) I can see that

var[X]=var[Y]=0.5 and that cov[X,Y]=0 because X and Y are independent

Your values 1/4, 1/4, 1/4 and 1/4 in your cells are only a particular solution. In fact, there a an infinite number of solutions: the general solution is p(-1,-1) = t, p(1, -1) = 0.5 - t, p(-1, 1) = 0.5 - t, p(1, 1) = t where t is a parameter and can have any value . Your particular solution corresponds to t = 0.25.

So what "p=2p(1,1)" does is defines an alternative parameter to express the general solution. My t corresponds p/2.